Philosophy and Goals of Contemporary College Algebra

Philosophy

Educate students for the future rather than train them for the past.

Primary Goal

Empower students to become exploratory learners, not to master a list of algebraic rules. Each section contains Queries that engage students in questioning and exploring the material being presented. Exercises that explicitly ask students to explore, ask what-if type questions, make up examples, further investigate worked examples, iterate for the purpose of recognizing a pattern and developing a sense for the behavior of a solution, and graphically fit a curve to a data set are some of the means that are used to establish an exploratory environment for the students.

Other Goals

1. Improve communication skills — reading, writing, presenting, listening.

   The large majority of the exercises are presented in the story problem format to address the reading aspect of this goal. The story problem format also addresses the applicability aspect of college algebra, as real-life situations are usually described verbally or in written form rather than in terms of equations.

2. Small-group work — in-class group activities and out-of-class group projects. In-class activities culminate in student presentations to the class, and out-of-class projects culminate in both a written report and a student presentation.

3. Use of technology — every student is expected to have daily access to a graphing calculator and/or computer. The ability to use technology for plotting and computation is a very important skill.

4. Modeling — to empower students to use mathematics to quantify real-life situations.

5. Confidence — develop personal confidence as a problem solver. Develop confidence in the iterative process: "try something, note the errors, modify previous attempt to lessen the errors, and try again" until a satisfactory approximation has been obtained. The initial attempt is usually informed by sketching a picture.

6. Enjoy applying mathematics to meaningful situations.